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Targeting hot spots of crime tends to disproportionately burden minority communities. Using stop, question and frisk data from New York City, I explicitly show this trade off by formulating a spatial allocation strategy that either prioritizes areas of high crime, or areas where stop arrest rates are high. I subsequently constrain the model to only allocate resources given different levels of acceptable racial inequality, as measured via the proportion of minorities likely to be stopped in those prioritized areas. I show that police stops can be both more efficiently and equitably distributed in New York City, but there are fundamental trade offs. One cannot gain a racial distribution completely equal to the residential population without large decreases in the efficiency of both targeting high crime areas and areas with high arrest rates.